Fluids
are some one which can flow from one place to other and both liquids and gases
falls under this category. Fluids in the state of rest and their properties
were studied in fluid statics and as we deal more about water, it is also
called as hydro statics. Fluids in the state of motion are studied in fluid
dynamics. Apart from pressure, here we need to talk about their energies also.
They have potential energy,kinetic energy and pressure energy and satisfy law
of conservation of energy. That is explained in terms of Bernoullie’s theorem.
If the density of the fluid is constant they are called in compressible. We can
ignore their viscous property and they are then called non viscous fluids.

**Problem**

A
horizontal pipe of non uniform area of cross section has water flows through it
at a point with a speed of 2 meter per second where the pressures is 40 kilo
pascal. We need to know the pressure at a point where the velocity is 3 meter
per second.

**Solution**

As
the tube is horizontal, there is no potential difference between the two
points. We need to apply Bernoullie’s theorem according to which the total
energy of the system that is the sum of potential energy,kinetic energy and
pressure energy is the constant. If one energy increases, other energy
decreases but their sum remains constant.

We
can apply this with the given data barring potential energy part as it is same
on both the sides and we can solve the problem as shown in the diagram below.

**Problem**

Two
water pipes of diameters 4 and 8 centimeter are connected in series to a main
pipe we need to find the ratio of velocities of the water in these two pipes
and the problem is as shown in the diagram below.

**Solution**

We
know that as the two pipes are connected in series the rate of flow of water is
same in both of them and hence the equation of continuity is very well valid
concept here. According to it the volume of the water passes through a given
system is always constant. It is nothing but the product of area of cross
section of the pipe and the velocity of the pipe is constant. Area can be
written as circular and it is proportional to the square of radius or diameter.
Problem can be further solved as shown in the diagram below.

Problem

Two
equal drops of water are falling through
with a velocity 10 meter per second and that is constant. If these two drops
are combined together and a single drop is formed, we need to find the velocity
of that combined drop and the problem is as shown in the diagram below.

**Solution**

The
constant velocity acquired by a spherical drop while passing through a medium
is called terminal velocity and at that instant the resultant force acting on
the system is zero. We have proved earlier in this chapter concepts that the
terminal velocity is directly proportional to the square of the radius of the
drop.

When
two drops are combined as both of them are of same density, its total volume is
the sum of the volumes of two drops. Taking that into consideration, we can
find the relation between small and large radius and the problem can be solved
as shown in the diagram below.

**Problem**

A
large tank is filled up to certain height and we need to know the ratio of time
taken by a small hole placed at the bottom to empty first half of the height of
the water when compared with the second height of the water. The problem is as
shown in the diagram below.

**Solution**

We
can prove and we have proved while handling this chapter that time taken to
empty the tank is directly proportional to the difference of height of fluid
from where to where they are emptied in terms of heights of fluid under square
root. In the first case, it is emptied from full to half and in the second
case, it is emptied from half to zero. By writing that data, we can solve the
problem as shown in the diagram below.

**Related Posts**

**Problems on Bernoulli's theorem and Its Applications**

## No comments:

## Post a Comment